What is the difference in energy between the two chair conformations of cis-1,2-dimethylcyclohexane? Cis-1,2-substitution in a chair cyclohexane means that one group (methyl) group must be equatorial and the other axial [Review]. A chair-chair interconversion would merely switch the position of the two groups: equatorial ---> axial; axial ---> equatorial. Therefore, ΔG^o = 0 kcal/mol and K_eq = 1. In fact, the two chairs are mirror images of one another. [Do not consider the red/blue of the methyl groups.] Rotate and arrange them so that they reflect one another as nearly as possible.

What is the energy of these mirror images? The red carbons illustrate the presence of a gauche butane interaction [Review: butane] between the two methyl groups (0.9 kcal/mol). Rotate the structure into a Newman projection to see the 60^o dihedral angle. The red axial methyl group has two gauche butane interactions with the ring, i. e., the red axial methyl group is diaxial to two hydrogens [Review]. The total energy is 1.8 + 0.9 = 3 x 0.9 = 2.7 kcal/mol.

What other chair dimethyl cyclohexanes have K_eq = 1? Click here for the answer.